Question

1,2 задание (желательно подробно)

Answer 1

$1)\; \; sin2x=-\frac{\sqrt2}{2}\\\\2x=(-1)^{n}\cdot (-\frac{\pi }{4})+\pi n=(-1)^{n+1}\cdot \frac{\pi }{4}+\pi n\; ,\; n\in Z\\\\x=(-1)^{n+1}\cdot \frac{\pi }{8}+\frac{\pi n}{2}=(-1)^{n+1}\cdot 22,5^\circ +90^\circ\cdot n\; ,\; n\in Z\\\\x\in (90^\circ ;270^\circ ):\; x=112,5^\circ \; ;\; 157,5^\circ \; .\\\\2)\; \; cos\frac{x}{2}=\frac{\sqrt3}{2}\\\\\frac{x}{2}=\pm \frac{\pi }{6}+2\pi n\; ,\; n\in Z\\\\x=\pm \frac{\pi }{3}+\pi n=\pm 60^\circ +180^\circ \cdot n\; ,\; n\in Z\\\\x\in (0^\circ \, ;\, 180^\circ ):\; \; x=60^\circ \; ;\; 120^\circ$